Question

Match the inequality to the number line that represents its solution.

Answer 1

Answer with explanation:

1)

$\dfrac{7x}{9}>\dfrac{-14}{3}$

On solving we get:

$x>-6$

Hence, the shaded region is to the right of -6 with open circle at -6.

2)

$\dfrac{-75x}{4}>\dfrac{225}{2}$

On solving we get:

$-x>\dfrac{225}{2}\times \dfrac{4}{75}\\\\\\-x>6$

on multiplying both side of the inequality by -1 we get:

$x$

Hence, the shaded region will be to the left of -6 and open circle at -6.

( Since, the inequality is strict)

3)

$\dfrac{x}{4}\leq \dfrac{-3}{2}\\\\\\x\leq \dfrac{-3}{2}\times 4\\\\\\x\leq -6$

The graph of this will be  shaded region to the left of -6 and closed circle at -6.

Since the inequality is an inequality with a equality sign.

4)

$\dfrac{2x}{3}>\dfrac{-16}{3}\\\\\\x>\dfrac{-16}{3}\times \dfrac{3}{2}\\\\\\x>-8$

Hence, the graph is a number line with shaded region to the right of -8 and open circle at -8.

( Since, the inequality is strict )

Answer 2

Tile 1=pair 2
tile 2=pair 4
tile 3=pair 1
tile 4=pair 3